Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


**Figure 13.**- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.


**Figure 13.**- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_pH 12 4.862001
beta2_pH 13 1.994913
beta0_pH 15 1.906881
beta3_black 1 1.805957
mu_beta0_pH 2 1.723223
beta2_black 2 1.502667
beta1_pH 19 1.406697
beta3_yellow 1 1.374419
beta1_black 7 1.334046
beta1_yellow 2 1.244050
parameter n badRhat_avg
beta2_pelagic 4 1.234800
beta2_yellow 3 1.218311
beta_H 1 1.209598
beta0_pelagic 1 1.172299
tau_beta0_yellow 3 1.166129
beta3_pelagic 1 1.157896
tau_beta0_pH 1 1.140238
beta0_yellow 1 1.125895
beta1_pelagic 2 1.125873
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta_H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
beta0_pelagic 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
beta0_pH 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 0
beta0_yellow 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
beta1_black 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0
beta1_pelagic 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1
beta1_pH 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
beta1_yellow 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0
beta2_black 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0
beta2_pelagic 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0
beta2_pH 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0
beta2_yellow 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0
beta3_black 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
beta3_pelagic 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
beta3_pH 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0
beta3_yellow 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
mu_beta0_pH 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
tau_beta0_pH 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.139 0.070 -0.278 -0.138 0.002
mu_bc_H[2] -0.099 0.044 -0.176 -0.102 0.000
mu_bc_H[3] -0.432 0.072 -0.569 -0.434 -0.287
mu_bc_H[4] -0.996 0.195 -1.393 -0.990 -0.619
mu_bc_H[5] 0.861 0.884 -0.196 0.677 2.957
mu_bc_H[6] -2.203 0.329 -2.854 -2.208 -1.543
mu_bc_H[7] -0.468 0.110 -0.689 -0.467 -0.254
mu_bc_H[8] 0.253 0.368 -0.350 0.216 1.105
mu_bc_H[9] -0.310 0.134 -0.580 -0.310 -0.046
mu_bc_H[10] -0.114 0.070 -0.237 -0.117 0.038
mu_bc_H[11] -0.107 0.041 -0.185 -0.107 -0.025
mu_bc_H[12] -0.249 0.104 -0.468 -0.249 -0.051
mu_bc_H[13] -0.120 0.079 -0.273 -0.120 0.037
mu_bc_H[14] -0.278 0.095 -0.474 -0.278 -0.086
mu_bc_H[15] -0.344 0.053 -0.446 -0.346 -0.236
mu_bc_H[16] -0.284 0.403 -0.980 -0.316 0.622
mu_bc_R[1] 1.352 0.145 1.065 1.352 1.640
mu_bc_R[2] 1.493 0.087 1.322 1.494 1.665
mu_bc_R[3] 1.424 0.136 1.158 1.422 1.682
mu_bc_R[4] 0.988 0.195 0.590 0.995 1.337
mu_bc_R[5] 1.145 0.454 0.247 1.147 2.022
mu_bc_R[6] -1.568 0.442 -2.461 -1.559 -0.715
mu_bc_R[7] 0.300 0.198 -0.105 0.302 0.685
mu_bc_R[8] 0.538 0.200 0.128 0.541 0.919
mu_bc_R[9] 0.383 0.194 -0.031 0.397 0.725
mu_bc_R[10] 1.334 0.125 1.084 1.339 1.562
mu_bc_R[11] 1.138 0.077 0.988 1.138 1.294
mu_bc_R[12] 0.951 0.199 0.557 0.947 1.344
mu_bc_R[13] 1.044 0.100 0.857 1.044 1.244
mu_bc_R[14] 0.975 0.146 0.691 0.974 1.263
mu_bc_R[15] 0.887 0.097 0.694 0.889 1.076
mu_bc_R[16] 1.204 0.119 0.968 1.209 1.432
tau_pH[1] 2.802 0.278 2.305 2.791 3.387
tau_pH[2] 2.775 0.355 2.116 2.764 3.507
tau_pH[3] 2.840 0.406 2.114 2.819 3.693
tau_pH[4] 6.421 1.243 4.277 6.308 9.065
beta0_pH[1,1] 0.526 0.219 0.068 0.536 0.935
beta0_pH[2,1] 1.279 0.240 0.812 1.290 1.747
beta0_pH[3,1] 1.380 0.260 0.843 1.390 1.865
beta0_pH[4,1] 1.622 0.273 1.050 1.640 2.093
beta0_pH[5,1] -0.401 0.540 -1.273 -0.474 1.009
beta0_pH[6,1] 0.099 0.551 -0.954 0.110 1.012
beta0_pH[7,1] 0.262 0.585 -0.826 0.487 1.000
beta0_pH[8,1] -0.538 0.292 -1.189 -0.506 -0.040
beta0_pH[9,1] -0.471 0.278 -1.043 -0.461 0.051
beta0_pH[10,1] 0.251 0.261 -0.297 0.255 0.750
beta0_pH[11,1] 0.138 0.699 -0.818 -0.089 1.798
beta0_pH[12,1] 0.528 0.273 -0.043 0.544 1.035
beta0_pH[13,1] 0.187 0.441 -0.550 0.129 1.127
beta0_pH[14,1] -0.003 0.692 -0.934 -0.252 1.450
beta0_pH[15,1] 0.151 0.715 -1.011 0.112 1.487
beta0_pH[16,1] 0.632 1.419 -1.447 -0.095 2.535
beta0_pH[1,2] 2.676 0.233 2.151 2.705 3.051
beta0_pH[2,2] 2.912 0.187 2.470 2.927 3.234
beta0_pH[3,2] 2.408 0.285 1.796 2.426 2.903
beta0_pH[4,2] 2.662 0.257 1.968 2.719 3.012
beta0_pH[5,2] 4.405 1.466 2.232 4.190 7.997
beta0_pH[6,2] 2.809 0.312 2.217 2.826 3.333
beta0_pH[7,2] 1.886 0.189 1.491 1.896 2.224
beta0_pH[8,2] 2.792 0.218 2.392 2.810 3.133
beta0_pH[9,2] 2.793 0.619 1.499 2.865 3.681
beta0_pH[10,2] 3.668 0.223 3.108 3.681 4.052
beta0_pH[11,2] -4.894 0.298 -5.486 -4.894 -4.307
beta0_pH[12,2] -4.873 0.472 -5.896 -4.846 -4.040
beta0_pH[13,2] -4.667 0.392 -5.497 -4.656 -3.920
beta0_pH[14,2] -5.649 0.480 -6.661 -5.619 -4.751
beta0_pH[15,2] -4.132 0.313 -4.765 -4.119 -3.546
beta0_pH[16,2] -4.866 0.375 -5.649 -4.853 -4.154
beta0_pH[1,3] 1.285 0.329 0.540 1.320 1.744
beta0_pH[2,3] 1.904 0.407 0.894 2.009 2.432
beta0_pH[3,3] 2.061 0.428 1.147 2.112 2.687
beta0_pH[4,3] 2.415 0.572 1.150 2.601 3.125
beta0_pH[5,3] 0.394 2.804 -4.538 0.710 5.937
beta0_pH[6,3] -1.031 1.489 -2.627 -1.503 2.936
beta0_pH[7,3] -1.982 1.024 -3.827 -2.038 0.700
beta0_pH[8,3] 0.303 0.179 -0.042 0.299 0.656
beta0_pH[9,3] -0.006 0.367 -0.687 0.007 0.670
beta0_pH[10,3] 0.776 0.362 0.068 0.809 1.310
beta0_pH[11,4] -0.370 0.572 -1.561 -0.287 0.726
beta0_pH[12,4] -0.538 0.639 -1.829 -0.495 0.579
beta0_pH[13,4] -0.457 0.666 -1.659 -0.474 0.943
beta0_pH[14,4] -0.527 0.524 -1.593 -0.566 0.597
beta0_pH[15,4] -0.449 0.507 -1.574 -0.401 0.504
beta0_pH[16,4] -0.451 0.839 -1.725 -0.567 1.919
beta0_pH[11,5] -0.755 0.196 -1.148 -0.750 -0.378
beta0_pH[12,5] -2.179 0.395 -2.756 -2.239 -1.305
beta0_pH[13,5] -0.092 0.266 -0.509 -0.133 0.552
beta0_pH[14,5] -0.989 0.199 -1.365 -0.997 -0.578
beta0_pH[15,5] -1.117 0.178 -1.456 -1.126 -0.766
beta0_pH[16,5] -1.019 0.896 -3.405 -0.676 -0.294
beta1_pH[1,1] 3.139 0.399 2.453 3.104 4.011
beta1_pH[2,1] 2.539 0.464 1.778 2.485 3.623
beta1_pH[3,1] 2.666 0.577 1.848 2.564 4.182
beta1_pH[4,1] 3.107 0.662 2.218 2.985 4.853
beta1_pH[5,1] 2.024 0.608 0.683 2.022 3.224
beta1_pH[6,1] 2.636 0.872 1.337 2.506 4.707
beta1_pH[7,1] 2.139 1.049 0.294 2.123 4.496
beta1_pH[8,1] 3.305 0.857 2.124 3.149 5.486
beta1_pH[9,1] 2.136 0.404 1.440 2.112 3.001
beta1_pH[10,1] 2.385 0.390 1.721 2.358 3.257
beta1_pH[11,1] 6.567 1.287 4.353 6.390 9.678
beta1_pH[12,1] 2.844 0.321 2.234 2.822 3.532
beta1_pH[13,1] 5.660 1.305 3.760 5.412 8.980
beta1_pH[14,1] 15.222 4.838 8.607 14.178 27.122
beta1_pH[15,1] 8.169 2.013 4.779 7.996 12.391
beta1_pH[16,1] 12.400 3.747 7.085 12.215 19.475
beta1_pH[1,2] 25.477 44.086 0.011 1.569 159.749
beta1_pH[2,2] 11.592 18.770 0.027 3.096 71.581
beta1_pH[3,2] 1.282 0.513 0.696 1.243 1.972
beta1_pH[4,2] 35.238 46.984 0.037 4.982 152.991
beta1_pH[5,2] 15.701 66.656 0.000 0.585 194.250
beta1_pH[6,2] 1.310 1.985 0.000 1.101 4.861
beta1_pH[7,2] 1.083 3.037 0.000 0.176 9.234
beta1_pH[8,2] 1.259 4.834 0.000 0.118 11.553
beta1_pH[9,2] 1.190 3.056 0.000 0.928 2.891
beta1_pH[10,2] 33.669 49.809 0.000 5.377 204.047
beta1_pH[11,2] 6.809 0.338 6.157 6.804 7.483
beta1_pH[12,2] 6.796 0.620 5.791 6.726 8.153
beta1_pH[13,2] 7.149 0.435 6.360 7.116 8.055
beta1_pH[14,2] 7.547 0.506 6.631 7.528 8.614
beta1_pH[15,2] 6.685 0.336 6.068 6.676 7.395
beta1_pH[16,2] 7.591 0.405 6.827 7.575 8.444
beta1_pH[1,3] 2.009 0.573 1.207 1.946 3.305
beta1_pH[2,3] 0.912 2.259 0.001 0.522 4.506
beta1_pH[3,3] 1.072 2.907 0.001 0.603 5.288
beta1_pH[4,3] 1.086 3.659 0.001 0.579 4.646
beta1_pH[5,3] 15.813 33.611 1.037 3.994 124.288
beta1_pH[6,3] 77.378 109.875 1.466 3.918 281.056
beta1_pH[7,3] 2.848 1.047 0.257 2.856 4.665
beta1_pH[8,3] 2.719 0.330 2.083 2.723 3.373
beta1_pH[9,3] 2.086 0.424 1.266 2.085 2.848
beta1_pH[10,3] 2.615 0.431 1.934 2.576 3.507
beta1_pH[11,4] 2.992 0.507 2.075 2.928 4.096
beta1_pH[12,4] 3.487 0.625 2.387 3.432 4.778
beta1_pH[13,4] 3.005 0.524 1.949 3.013 3.963
beta1_pH[14,4] 2.947 0.485 1.936 2.971 3.941
beta1_pH[15,4] 2.943 0.518 2.082 2.902 4.038
beta1_pH[16,4] 3.099 0.959 2.049 2.912 5.150
beta1_pH[11,5] 2.868 0.932 1.717 2.779 4.454
beta1_pH[12,5] 3.758 1.158 2.448 3.517 6.596
beta1_pH[13,5] 3.527 1.135 2.296 3.299 5.998
beta1_pH[14,5] 3.121 1.007 1.874 2.974 5.538
beta1_pH[15,5] 3.126 1.180 1.922 2.951 5.365
beta1_pH[16,5] 3.127 0.925 1.457 3.039 5.148
beta2_pH[1,1] 0.483 0.232 0.248 0.451 0.861
beta2_pH[2,1] 0.465 0.291 0.166 0.408 1.113
beta2_pH[3,1] 0.419 0.256 0.152 0.369 0.984
beta2_pH[4,1] 0.371 0.160 0.159 0.342 0.747
beta2_pH[5,1] 0.956 1.260 0.038 0.471 4.794
beta2_pH[6,1] 0.661 1.091 0.111 0.311 3.722
beta2_pH[7,1] -0.428 1.268 -4.148 -0.006 1.062
beta2_pH[8,1] 0.387 0.467 0.149 0.300 1.064
beta2_pH[9,1] 0.612 0.637 0.168 0.441 2.251
beta2_pH[10,1] 0.651 0.661 0.214 0.498 2.137
beta2_pH[11,1] 0.231 0.061 0.130 0.225 0.374
beta2_pH[12,1] 1.098 0.603 0.434 0.960 2.636
beta2_pH[13,1] 0.269 0.078 0.156 0.259 0.457
beta2_pH[14,1] 0.277 0.078 0.183 0.256 0.478
beta2_pH[15,1] 0.216 0.097 0.132 0.200 0.371
beta2_pH[16,1] 0.420 0.373 0.119 0.194 1.306
beta2_pH[1,2] -2.382 4.002 -10.102 -2.609 5.579
beta2_pH[2,2] -3.697 2.917 -10.495 -3.218 0.593
beta2_pH[3,2] -3.973 2.695 -11.209 -3.393 -0.619
beta2_pH[4,2] -3.939 2.756 -10.332 -3.487 -0.142
beta2_pH[5,2] -2.227 3.828 -9.619 -2.302 5.554
beta2_pH[6,2] -3.169 3.191 -9.750 -2.965 3.818
beta2_pH[7,2] -3.108 3.490 -10.013 -3.076 4.847
beta2_pH[8,2] -2.887 3.633 -10.000 -3.012 5.243
beta2_pH[9,2] -3.238 3.419 -10.398 -3.121 4.662
beta2_pH[10,2] -3.903 3.268 -11.110 -3.787 3.615
beta2_pH[11,2] -6.749 2.498 -13.159 -6.280 -3.273
beta2_pH[12,2] -2.864 2.516 -9.399 -1.728 -0.558
beta2_pH[13,2] -3.573 2.109 -9.528 -2.882 -1.329
beta2_pH[14,2] -4.714 2.414 -10.812 -4.139 -1.694
beta2_pH[15,2] -6.514 2.449 -12.679 -5.975 -3.244
beta2_pH[16,2] -6.981 2.616 -13.668 -6.413 -3.425
beta2_pH[1,3] 3.546 2.582 0.310 3.016 10.176
beta2_pH[2,3] 2.219 3.731 -5.677 2.220 9.755
beta2_pH[3,3] 1.717 4.294 -7.673 2.007 9.225
beta2_pH[4,3] 2.242 3.708 -5.508 2.167 9.797
beta2_pH[5,3] 5.181 3.012 0.470 4.849 11.988
beta2_pH[6,3] 5.202 2.896 0.694 4.884 11.925
beta2_pH[7,3] 4.963 3.003 0.619 4.597 12.111
beta2_pH[8,3] 6.369 2.742 2.203 5.985 12.733
beta2_pH[9,3] 5.365 2.699 1.363 4.999 11.836
beta2_pH[10,3] 4.657 2.664 0.641 4.308 10.344
beta2_pH[11,4] -1.290 4.672 -10.502 -1.543 7.317
beta2_pH[12,4] -3.155 2.668 -10.259 -2.103 -0.681
beta2_pH[13,4] -0.837 3.872 -10.283 0.585 4.639
beta2_pH[14,4] -0.427 4.860 -9.820 -1.284 8.770
beta2_pH[15,4] -0.425 3.606 -9.299 0.977 4.373
beta2_pH[16,4] -1.416 4.872 -10.225 -2.023 8.275
beta2_pH[11,5] -3.092 2.499 -9.840 -2.215 -0.652
beta2_pH[12,5] -3.910 2.805 -11.538 -2.790 -1.011
beta2_pH[13,5] -4.180 2.452 -10.523 -3.538 -1.316
beta2_pH[14,5] -4.643 2.681 -11.277 -4.036 -1.207
beta2_pH[15,5] -4.694 2.371 -10.670 -4.153 -1.546
beta2_pH[16,5] -2.736 3.491 -10.217 -2.491 5.128
beta3_pH[1,1] 35.799 1.109 33.744 35.745 38.072
beta3_pH[2,1] 34.450 1.971 31.369 34.148 38.848
beta3_pH[3,1] 36.027 2.146 32.681 35.755 41.365
beta3_pH[4,1] 36.211 1.949 32.961 35.989 40.700
beta3_pH[5,1] 29.908 4.141 21.476 28.852 40.707
beta3_pH[6,1] 40.279 3.457 32.803 41.127 45.298
beta3_pH[7,1] 29.112 9.121 18.420 25.955 45.606
beta3_pH[8,1] 38.984 2.084 34.870 38.977 43.527
beta3_pH[9,1] 31.280 2.119 27.780 31.087 36.259
beta3_pH[10,1] 32.926 1.323 30.588 32.844 35.752
beta3_pH[11,1] 36.766 2.449 33.213 36.186 42.654
beta3_pH[12,1] 30.436 0.587 29.218 30.457 31.476
beta3_pH[13,1] 39.418 2.239 35.636 39.214 44.478
beta3_pH[14,1] 41.897 1.937 38.426 41.744 45.573
beta3_pH[15,1] 41.324 2.579 36.520 41.387 45.699
beta3_pH[16,1] 44.208 1.406 40.475 44.540 45.925
beta3_pH[1,2] 29.259 8.602 18.378 27.027 44.037
beta3_pH[2,2] 27.992 5.162 18.879 28.107 40.691
beta3_pH[3,2] 41.632 2.096 39.553 41.826 43.845
beta3_pH[4,2] 27.195 8.076 18.412 24.191 43.362
beta3_pH[5,2] 30.627 8.048 18.535 29.604 44.940
beta3_pH[6,2] 33.577 5.697 19.144 35.204 44.032
beta3_pH[7,2] 29.458 7.418 18.582 28.736 44.661
beta3_pH[8,2] 28.608 7.357 18.388 27.164 44.238
beta3_pH[9,2] 37.801 9.038 19.177 43.431 45.728
beta3_pH[10,2] 29.311 5.401 19.042 29.174 41.747
beta3_pH[11,2] 43.366 0.143 43.133 43.346 43.693
beta3_pH[12,2] 43.131 0.262 42.534 43.149 43.630
beta3_pH[13,2] 43.840 0.146 43.522 43.855 44.095
beta3_pH[14,2] 43.312 0.158 43.075 43.291 43.667
beta3_pH[15,2] 43.394 0.156 43.139 43.380 43.718
beta3_pH[16,2] 43.486 0.160 43.199 43.483 43.799
beta3_pH[1,3] 39.985 0.978 37.661 40.056 41.389
beta3_pH[2,3] 31.387 7.367 18.681 32.406 44.918
beta3_pH[3,3] 30.967 6.968 18.761 31.902 43.731
beta3_pH[4,3] 27.529 6.921 18.341 26.536 44.225
beta3_pH[5,3] 26.867 5.584 18.487 27.212 40.725
beta3_pH[6,3] 30.815 4.614 20.095 31.809 40.937
beta3_pH[7,3] 25.664 2.783 22.372 24.933 31.425
beta3_pH[8,3] 41.495 0.226 41.095 41.494 41.919
beta3_pH[9,3] 33.755 0.491 32.944 33.770 34.734
beta3_pH[10,3] 36.043 0.577 34.646 36.105 36.819
beta3_pH[11,4] 39.117 7.034 29.068 43.401 45.853
beta3_pH[12,4] 42.068 0.636 40.865 42.085 42.952
beta3_pH[13,4] 35.157 5.994 29.742 31.267 44.514
beta3_pH[14,4] 38.228 6.266 29.256 41.734 45.451
beta3_pH[15,4] 34.902 6.799 29.317 30.280 45.841
beta3_pH[16,4] 39.230 6.967 29.159 43.437 45.866
beta3_pH[11,5] 40.224 0.755 38.963 40.148 42.073
beta3_pH[12,5] 38.789 1.510 36.584 38.587 42.648
beta3_pH[13,5] 41.018 0.521 40.200 40.950 42.676
beta3_pH[14,5] 39.892 0.779 38.957 39.701 42.204
beta3_pH[15,5] 40.738 0.337 40.133 40.756 41.364
beta3_pH[16,5] 38.235 3.674 29.181 39.523 41.680
beta0_pelagic[1] 1.706 0.540 0.447 1.845 2.374
beta0_pelagic[2] 1.144 0.453 0.089 1.279 1.720
beta0_pelagic[3] 0.277 0.302 -0.501 0.312 0.741
beta0_pelagic[4] 0.048 0.612 -1.633 0.196 0.890
beta0_pelagic[5] 0.254 1.527 -3.071 1.179 1.633
beta0_pelagic[6] 1.505 0.312 0.622 1.564 1.835
beta0_pelagic[7] 1.525 0.147 1.231 1.532 1.792
beta0_pelagic[8] 1.841 0.166 1.513 1.855 2.103
beta0_pelagic[9] 1.919 0.835 -0.115 2.053 2.846
beta0_pelagic[10] 2.505 0.313 1.656 2.557 2.817
beta0_pelagic[11] 0.669 0.145 0.358 0.674 0.939
beta0_pelagic[12] 1.759 0.133 1.501 1.760 2.015
beta0_pelagic[13] 0.562 0.149 0.261 0.564 0.847
beta0_pelagic[14] 0.417 0.187 0.010 0.429 0.751
beta0_pelagic[15] -0.246 0.131 -0.502 -0.246 0.018
beta0_pelagic[16] 0.547 0.123 0.303 0.550 0.789
beta1_pelagic[1] 0.544 0.547 0.000 0.424 1.841
beta1_pelagic[2] 0.439 0.447 0.000 0.321 1.497
beta1_pelagic[3] 0.784 0.351 0.217 0.744 1.768
beta1_pelagic[4] 1.145 0.617 0.251 1.001 2.864
beta1_pelagic[5] 1.200 1.644 0.000 0.024 4.728
beta1_pelagic[6] 0.160 0.404 0.000 0.003 1.371
beta1_pelagic[7] 1.461 5.396 0.000 0.004 13.984
beta1_pelagic[8] 0.333 1.664 0.000 0.003 1.887
beta1_pelagic[9] 0.976 1.046 0.000 0.913 3.699
beta1_pelagic[10] 0.282 1.434 0.000 0.002 2.343
beta1_pelagic[11] 2.407 0.299 1.882 2.389 3.037
beta1_pelagic[12] 2.631 0.270 2.110 2.622 3.178
beta1_pelagic[13] 2.272 0.441 1.530 2.225 3.269
beta1_pelagic[14] 3.133 0.681 2.117 3.005 4.842
beta1_pelagic[15] 2.513 0.243 2.048 2.519 2.992
beta1_pelagic[16] 2.996 0.261 2.502 2.990 3.512
beta2_pelagic[1] 2.221 2.224 -1.600 1.806 7.776
beta2_pelagic[2] 2.263 2.502 -1.728 1.686 8.549
beta2_pelagic[3] 2.234 2.236 0.144 1.454 8.330
beta2_pelagic[4] 2.114 2.145 0.222 1.328 7.968
beta2_pelagic[5] -1.180 3.727 -8.316 -1.706 6.924
beta2_pelagic[6] 0.349 3.648 -8.333 0.595 8.081
beta2_pelagic[7] -0.531 4.277 -9.322 -0.170 8.056
beta2_pelagic[8] -0.456 4.124 -7.776 -0.375 8.189
beta2_pelagic[9] 1.122 3.498 -6.834 0.928 8.396
beta2_pelagic[10] -0.004 4.031 -8.448 0.272 8.011
beta2_pelagic[11] 4.081 2.756 0.373 3.534 10.868
beta2_pelagic[12] 5.420 2.618 1.929 4.877 11.723
beta2_pelagic[13] 1.654 2.082 0.314 0.871 7.581
beta2_pelagic[14] 0.595 0.563 0.234 0.469 1.760
beta2_pelagic[15] 5.128 2.546 2.355 4.092 11.642
beta2_pelagic[16] 5.228 2.956 1.126 4.718 12.320
beta3_pelagic[1] 25.615 6.496 18.444 23.073 42.829
beta3_pelagic[2] 25.262 7.116 18.215 22.546 43.971
beta3_pelagic[3] 29.634 4.110 22.700 29.671 41.252
beta3_pelagic[4] 24.584 2.836 19.881 24.580 30.320
beta3_pelagic[5] 35.763 9.907 18.631 37.959 45.991
beta3_pelagic[6] 30.085 8.007 18.554 29.137 45.093
beta3_pelagic[7] 28.384 8.324 18.425 26.434 44.770
beta3_pelagic[8] 27.568 7.327 18.389 26.083 44.117
beta3_pelagic[9] 28.955 6.191 19.119 27.009 43.745
beta3_pelagic[10] 29.172 8.266 18.306 27.508 45.002
beta3_pelagic[11] 43.201 0.452 42.161 43.226 43.882
beta3_pelagic[12] 43.464 0.229 43.052 43.452 43.917
beta3_pelagic[13] 42.720 0.963 40.742 42.803 44.662
beta3_pelagic[14] 43.022 1.254 40.492 43.023 45.522
beta3_pelagic[15] 43.233 0.209 42.798 43.225 43.657
beta3_pelagic[16] 43.244 0.265 42.584 43.258 43.701
mu_beta0_pelagic[1] 0.739 0.818 -1.014 0.742 2.393
mu_beta0_pelagic[2] 1.538 0.691 -0.283 1.681 2.545
mu_beta0_pelagic[3] 0.613 0.413 -0.223 0.617 1.421
tau_beta0_pelagic[1] 2.090 5.948 0.062 0.751 11.145
tau_beta0_pelagic[2] 2.648 4.990 0.082 1.392 11.293
tau_beta0_pelagic[3] 1.901 1.462 0.234 1.552 5.661
beta0_yellow[1] -0.534 0.185 -0.939 -0.515 -0.234
beta0_yellow[2] 0.497 0.166 0.160 0.508 0.794
beta0_yellow[3] -0.321 0.199 -0.698 -0.309 0.014
beta0_yellow[4] 0.799 0.329 -0.259 0.866 1.187
beta0_yellow[5] -1.209 0.401 -1.999 -1.212 -0.443
beta0_yellow[6] 0.252 0.209 -0.158 0.250 0.668
beta0_yellow[7] 0.837 0.585 -0.928 1.028 1.341
beta0_yellow[8] 0.702 0.642 -1.096 0.939 1.284
beta0_yellow[9] -0.073 0.272 -0.601 -0.070 0.422
beta0_yellow[10] 0.256 0.150 -0.030 0.252 0.554
beta0_yellow[11] -1.931 0.439 -2.836 -1.908 -1.092
beta0_yellow[12] -3.547 0.413 -4.403 -3.529 -2.800
beta0_yellow[13] -3.541 0.439 -4.481 -3.510 -2.765
beta0_yellow[14] -2.023 0.603 -3.000 -2.097 -0.258
beta0_yellow[15] -2.814 0.390 -3.659 -2.791 -2.084
beta0_yellow[16] -2.381 0.441 -3.256 -2.398 -1.470
beta1_yellow[1] 0.498 0.615 0.000 0.358 1.716
beta1_yellow[2] 1.057 0.330 0.593 1.020 1.952
beta1_yellow[3] 0.685 0.413 0.150 0.663 1.204
beta1_yellow[4] 1.471 0.929 0.656 1.197 4.501
beta1_yellow[5] 2.842 1.136 1.336 2.713 4.741
beta1_yellow[6] 2.277 0.347 1.615 2.280 2.983
beta1_yellow[7] 5.053 4.885 0.508 3.621 17.873
beta1_yellow[8] 2.393 2.171 0.080 1.947 8.193
beta1_yellow[9] 1.552 0.426 0.855 1.529 2.453
beta1_yellow[10] 2.445 0.531 1.376 2.436 3.543
beta1_yellow[11] 2.079 0.443 1.236 2.060 3.027
beta1_yellow[12] 2.331 0.426 1.594 2.309 3.220
beta1_yellow[13] 2.718 0.441 1.939 2.679 3.645
beta1_yellow[14] 2.135 0.521 0.963 2.158 3.060
beta1_yellow[15] 2.110 0.390 1.394 2.081 2.949
beta1_yellow[16] 2.194 0.439 1.315 2.202 3.071
beta2_yellow[1] -2.748 2.625 -8.595 -2.415 1.697
beta2_yellow[2] -3.053 1.973 -7.867 -3.120 -0.181
beta2_yellow[3] -3.029 2.434 -9.069 -2.527 -0.141
beta2_yellow[4] -2.532 2.456 -8.840 -1.941 -0.077
beta2_yellow[5] -4.439 2.927 -11.611 -3.939 -0.667
beta2_yellow[6] 3.672 2.264 0.963 3.152 9.348
beta2_yellow[7] -3.623 4.195 -11.384 -3.934 6.084
beta2_yellow[8] -2.138 4.184 -10.744 -1.971 6.740
beta2_yellow[9] 3.766 2.341 0.261 3.414 9.336
beta2_yellow[10] -4.884 2.747 -11.492 -4.384 -1.041
beta2_yellow[11] -4.042 2.310 -9.828 -3.467 -1.146
beta2_yellow[12] -4.032 2.161 -9.494 -3.526 -1.197
beta2_yellow[13] -4.187 2.187 -9.724 -3.645 -1.517
beta2_yellow[14] -4.023 2.310 -9.711 -3.554 -0.545
beta2_yellow[15] -4.242 2.476 -9.815 -3.504 -1.124
beta2_yellow[16] -4.285 2.255 -9.727 -3.722 -1.370
beta3_yellow[1] 27.981 7.496 18.364 26.135 44.409
beta3_yellow[2] 29.131 1.516 26.139 28.899 32.550
beta3_yellow[3] 32.972 3.083 25.059 32.949 39.175
beta3_yellow[4] 29.149 3.549 21.220 28.154 35.735
beta3_yellow[5] 33.476 1.254 31.167 33.448 35.729
beta3_yellow[6] 39.647 0.515 38.743 39.608 40.871
beta3_yellow[7] 21.266 3.348 18.612 20.198 30.336
beta3_yellow[8] 25.586 5.061 18.381 25.395 39.227
beta3_yellow[9] 37.774 1.734 36.168 37.598 42.723
beta3_yellow[10] 29.404 0.427 28.362 29.448 30.079
beta3_yellow[11] 45.411 0.458 44.260 45.505 45.977
beta3_yellow[12] 43.404 0.446 42.561 43.370 44.385
beta3_yellow[13] 44.845 0.393 44.012 44.913 45.507
beta3_yellow[14] 43.668 2.943 31.024 44.195 45.821
beta3_yellow[15] 45.297 0.501 44.211 45.343 45.981
beta3_yellow[16] 44.643 0.631 43.477 44.637 45.847
mu_beta0_yellow[1] 0.089 0.541 -0.991 0.089 1.252
mu_beta0_yellow[2] 0.116 0.487 -0.842 0.119 1.076
mu_beta0_yellow[3] -2.415 0.595 -3.347 -2.497 -0.982
tau_beta0_yellow[1] 1.926 3.305 0.087 1.152 7.347
tau_beta0_yellow[2] 1.512 2.516 0.151 1.041 5.345
tau_beta0_yellow[3] 1.729 3.041 0.114 1.038 6.931
beta0_black[1] -0.085 0.148 -0.375 -0.086 0.205
beta0_black[2] 1.844 0.186 1.441 1.866 2.111
beta0_black[3] 1.251 0.190 0.864 1.269 1.540
beta0_black[4] 2.001 0.312 1.432 2.033 2.431
beta0_black[5] 1.568 1.950 -3.015 1.615 5.488
beta0_black[6] 1.629 2.029 -3.140 1.638 5.790
beta0_black[7] 1.590 2.002 -3.040 1.626 5.897
beta0_black[8] 1.258 0.222 0.824 1.258 1.700
beta0_black[9] 2.413 0.267 1.891 2.418 2.881
beta0_black[10] 1.458 0.129 1.208 1.459 1.709
beta0_black[11] 3.408 0.231 2.926 3.432 3.738
beta0_black[12] 4.479 0.211 4.108 4.484 4.846
beta0_black[13] -0.096 0.219 -0.529 -0.092 0.333
beta0_black[14] 2.080 0.719 0.020 2.253 2.845
beta0_black[15] 1.146 0.345 0.284 1.214 1.550
beta0_black[16] 3.967 0.737 1.628 4.197 4.539
beta2_black[1] 3.600 2.379 0.788 3.043 9.177
beta2_black[2] -1.851 4.241 -8.263 -2.237 8.032
beta2_black[3] -0.133 4.395 -8.936 0.085 8.484
beta2_black[4] -3.887 3.542 -12.232 -2.875 -0.083
beta2_black[5] -0.369 4.231 -8.732 -0.455 7.905
beta2_black[6] -0.337 4.355 -8.622 -0.344 8.192
beta2_black[7] -0.289 4.273 -8.746 -0.437 8.149
beta2_black[8] -0.537 4.222 -8.952 -0.711 8.018
beta2_black[9] -0.450 4.302 -9.064 -0.565 8.073
beta2_black[10] -0.436 4.408 -8.986 -0.616 8.258
beta2_black[11] -2.412 2.418 -8.127 -2.006 1.767
beta2_black[12] -3.103 2.143 -8.551 -2.527 -0.579
beta2_black[13] -2.606 2.114 -8.358 -1.882 -0.520
beta2_black[14] -1.681 2.184 -7.630 -0.629 -0.060
beta2_black[15] -2.592 2.693 -9.625 -2.001 1.680
beta2_black[16] -1.635 3.061 -8.133 -1.322 4.803
beta3_black[1] 41.670 1.439 39.950 41.871 42.968
beta3_black[2] 29.932 8.047 18.348 29.782 44.718
beta3_black[3] 29.231 7.868 18.507 28.740 44.787
beta3_black[4] 33.037 3.114 23.309 32.777 38.121
beta3_black[5] 29.892 7.979 18.466 28.903 44.817
beta3_black[6] 29.680 7.902 18.512 28.499 44.732
beta3_black[7] 29.946 7.980 18.487 28.951 44.721
beta3_black[8] 30.213 7.951 18.452 29.383 44.919
beta3_black[9] 30.020 7.931 18.529 28.965 44.630
beta3_black[10] 29.813 7.846 18.507 28.931 44.700
beta3_black[11] 29.633 6.908 18.608 29.519 43.896
beta3_black[12] 32.743 1.174 29.638 32.950 33.878
beta3_black[13] 39.311 0.660 37.758 39.387 40.469
beta3_black[14] 34.049 7.759 18.395 37.273 44.174
beta3_black[15] 31.342 7.985 18.795 31.089 45.148
beta3_black[16] 28.763 7.515 18.419 27.431 44.523
beta4_black[1] -0.252 0.183 -0.611 -0.250 0.093
beta4_black[2] 0.249 0.169 -0.087 0.250 0.586
beta4_black[3] -0.930 0.185 -1.291 -0.930 -0.555
beta4_black[4] 0.548 0.218 0.140 0.545 0.994
beta4_black[5] 0.163 2.462 -4.563 0.118 5.025
beta4_black[6] 0.198 2.686 -4.730 0.184 5.083
beta4_black[7] 0.210 2.390 -4.369 0.104 5.216
beta4_black[8] -0.684 0.359 -1.394 -0.676 -0.007
beta4_black[9] 1.432 1.000 -0.113 1.308 3.755
beta4_black[10] 0.028 0.178 -0.319 0.027 0.379
beta4_black[11] -0.702 0.203 -1.097 -0.701 -0.315
beta4_black[12] 0.297 0.328 -0.335 0.293 0.956
beta4_black[13] -1.187 0.209 -1.590 -1.186 -0.772
beta4_black[14] -0.108 0.228 -0.554 -0.112 0.349
beta4_black[15] -0.897 0.202 -1.294 -0.892 -0.502
beta4_black[16] -0.602 0.220 -1.029 -0.601 -0.160
mu_beta0_black[1] 1.185 0.897 -0.796 1.213 2.993
mu_beta0_black[2] 1.583 0.932 -0.633 1.643 3.296
mu_beta0_black[3] 2.272 0.981 0.225 2.334 4.078
tau_beta0_black[1] 0.796 0.799 0.059 0.557 2.964
tau_beta0_black[2] 2.026 4.266 0.057 0.803 10.264
tau_beta0_black[3] 0.254 0.174 0.052 0.211 0.695
beta0_dsr[11] -3.018 0.274 -3.544 -3.022 -2.475
beta0_dsr[12] 4.476 0.270 3.951 4.470 5.006
beta0_dsr[13] -1.589 0.305 -2.172 -1.579 -1.028
beta0_dsr[14] -4.122 0.486 -5.098 -4.109 -3.219
beta0_dsr[15] -2.397 0.256 -2.917 -2.390 -1.892
beta0_dsr[16] -3.061 0.345 -3.741 -3.062 -2.383
beta1_dsr[11] 4.894 0.292 4.322 4.894 5.459
beta1_dsr[12] 6.211 5.719 2.306 5.156 15.695
beta1_dsr[13] 3.047 0.334 2.481 3.030 3.638
beta1_dsr[14] 6.758 0.511 5.802 6.750 7.774
beta1_dsr[15] 3.586 0.269 3.062 3.587 4.111
beta1_dsr[16] 5.848 0.364 5.122 5.848 6.584
beta2_dsr[11] -8.292 2.390 -14.030 -7.937 -4.696
beta2_dsr[12] -7.242 2.649 -13.018 -7.058 -2.520
beta2_dsr[13] -6.502 2.710 -12.366 -6.386 -1.674
beta2_dsr[14] -6.695 2.423 -12.018 -6.483 -2.559
beta2_dsr[15] -7.769 2.452 -13.551 -7.421 -3.849
beta2_dsr[16] -7.972 2.328 -13.602 -7.617 -4.446
beta3_dsr[11] 43.482 0.146 43.221 43.480 43.760
beta3_dsr[12] 34.006 0.664 32.275 34.163 34.806
beta3_dsr[13] 43.238 0.269 42.878 43.169 43.857
beta3_dsr[14] 43.258 0.143 43.081 43.222 43.635
beta3_dsr[15] 43.470 0.183 43.145 43.462 43.811
beta3_dsr[16] 43.431 0.155 43.179 43.411 43.744
beta4_dsr[11] 0.659 0.210 0.241 0.662 1.070
beta4_dsr[12] 0.307 0.468 -0.632 0.306 1.242
beta4_dsr[13] -0.086 0.210 -0.490 -0.082 0.321
beta4_dsr[14] 0.198 0.248 -0.278 0.199 0.678
beta4_dsr[15] 0.988 0.208 0.582 0.987 1.384
beta4_dsr[16] 0.177 0.220 -0.265 0.174 0.605
beta0_slope[11] -2.006 0.152 -2.307 -2.009 -1.712
beta0_slope[12] -4.674 0.260 -5.181 -4.677 -4.159
beta0_slope[13] -1.436 0.234 -2.029 -1.414 -1.076
beta0_slope[14] -2.631 0.206 -3.038 -2.634 -2.244
beta0_slope[15] -1.702 0.156 -2.014 -1.696 -1.407
beta0_slope[16] -2.750 0.170 -3.079 -2.746 -2.422
beta1_slope[11] 4.392 0.293 3.817 4.388 4.961
beta1_slope[12] 4.904 0.521 3.895 4.911 5.960
beta1_slope[13] 2.713 0.601 2.014 2.614 4.643
beta1_slope[14] 6.041 0.842 4.654 5.943 7.958
beta1_slope[15] 2.041 0.280 1.498 2.040 2.606
beta1_slope[16] 5.286 0.394 4.530 5.270 6.089
beta2_slope[11] 7.752 2.371 4.100 7.369 13.260
beta2_slope[12] 6.546 2.630 2.085 6.268 12.529
beta2_slope[13] 4.598 2.921 0.288 4.234 11.391
beta2_slope[14] 2.948 2.728 0.718 1.556 9.728
beta2_slope[15] 6.657 2.530 2.578 6.325 12.153
beta2_slope[16] 7.273 2.382 3.562 6.911 12.902
beta3_slope[11] 43.493 0.153 43.207 43.489 43.791
beta3_slope[12] 43.414 0.224 43.060 43.390 43.861
beta3_slope[13] 43.586 0.527 42.681 43.617 44.587
beta3_slope[14] 44.703 0.429 43.800 44.771 45.356
beta3_slope[15] 43.600 0.249 43.136 43.607 44.051
beta3_slope[16] 43.471 0.169 43.177 43.460 43.806
beta4_slope[11] -0.461 0.207 -0.867 -0.461 -0.070
beta4_slope[12] -1.248 0.669 -2.776 -1.168 -0.194
beta4_slope[13] 0.180 0.217 -0.228 0.175 0.594
beta4_slope[14] -0.126 0.247 -0.613 -0.130 0.357
beta4_slope[15] -0.204 0.197 -0.584 -0.207 0.189
beta4_slope[16] -0.141 0.225 -0.579 -0.144 0.302
sigma_H[1] 0.196 0.054 0.095 0.193 0.311
sigma_H[2] 0.171 0.029 0.119 0.169 0.234
sigma_H[3] 0.196 0.041 0.122 0.193 0.283
sigma_H[4] 0.414 0.076 0.288 0.405 0.584
sigma_H[5] 0.987 0.207 0.586 0.981 1.409
sigma_H[6] 0.361 0.199 0.026 0.352 0.791
sigma_H[7] 0.299 0.061 0.206 0.291 0.444
sigma_H[8] 0.427 0.099 0.277 0.414 0.639
sigma_H[9] 0.514 0.120 0.325 0.497 0.796
sigma_H[10] 0.218 0.041 0.146 0.214 0.307
sigma_H[11] 0.278 0.046 0.201 0.274 0.380
sigma_H[12] 0.440 0.162 0.211 0.417 0.761
sigma_H[13] 0.215 0.038 0.149 0.212 0.296
sigma_H[14] 0.509 0.094 0.339 0.503 0.705
sigma_H[15] 0.249 0.041 0.181 0.245 0.344
sigma_H[16] 0.225 0.044 0.151 0.221 0.322
lambda_H[1] 2.965 3.864 0.144 1.649 13.387
lambda_H[2] 8.066 7.312 0.805 5.997 27.646
lambda_H[3] 6.162 9.870 0.279 2.953 32.120
lambda_H[4] 0.007 0.004 0.001 0.005 0.018
lambda_H[5] 4.565 13.302 0.030 0.912 32.047
lambda_H[6] 7.631 15.132 0.007 0.691 53.608
lambda_H[7] 0.014 0.010 0.002 0.011 0.039
lambda_H[8] 8.337 10.275 0.011 4.699 37.845
lambda_H[9] 0.016 0.011 0.003 0.013 0.044
lambda_H[10] 0.324 0.735 0.034 0.196 1.148
lambda_H[11] 0.260 0.397 0.013 0.135 1.220
lambda_H[12] 4.815 6.089 0.205 2.809 21.742
lambda_H[13] 3.279 2.997 0.213 2.474 11.371
lambda_H[14] 3.577 4.254 0.238 2.151 15.499
lambda_H[15] 0.027 0.040 0.003 0.017 0.110
lambda_H[16] 1.356 2.031 0.064 0.707 6.262
mu_lambda_H[1] 4.354 1.895 1.257 4.183 8.346
mu_lambda_H[2] 3.841 1.980 0.570 3.729 8.053
mu_lambda_H[3] 3.584 1.878 0.792 3.333 7.775
sigma_lambda_H[1] 8.681 4.292 2.036 7.979 18.335
sigma_lambda_H[2] 8.379 4.671 0.953 7.819 18.261
sigma_lambda_H[3] 6.371 4.019 1.035 5.528 16.099
beta_H[1,1] 6.855 1.079 4.295 7.032 8.461
beta_H[2,1] 9.878 0.467 8.881 9.896 10.743
beta_H[3,1] 7.997 0.796 6.112 8.091 9.367
beta_H[4,1] 9.544 7.691 -6.147 9.673 24.185
beta_H[5,1] 0.125 2.332 -4.791 0.339 3.944
beta_H[6,1] 2.994 4.088 -7.100 4.434 7.582
beta_H[7,1] 0.938 5.803 -11.361 1.364 11.546
beta_H[8,1] 1.945 6.261 -2.401 1.338 9.116
beta_H[9,1] 13.088 5.724 1.658 13.096 24.390
beta_H[10,1] 7.131 1.761 3.546 7.152 10.654
beta_H[11,1] 5.337 3.426 -2.567 6.102 9.990
beta_H[12,1] 2.602 1.034 0.721 2.537 4.800
beta_H[13,1] 9.059 0.996 7.207 9.127 10.590
beta_H[14,1] 2.178 0.994 0.188 2.187 4.171
beta_H[15,1] -5.858 3.990 -12.950 -6.072 2.738
beta_H[16,1] 3.215 2.303 -0.697 3.019 8.702
beta_H[1,2] 7.905 0.243 7.413 7.910 8.351
beta_H[2,2] 10.027 0.135 9.754 10.027 10.291
beta_H[3,2] 8.950 0.201 8.561 8.951 9.355
beta_H[4,2] 3.493 1.456 0.768 3.419 6.573
beta_H[5,2] 1.997 0.956 0.166 2.016 3.866
beta_H[6,2] 5.727 1.094 3.139 5.912 7.392
beta_H[7,2] 2.520 1.099 0.545 2.440 4.881
beta_H[8,2] 2.886 1.577 -0.353 3.149 4.225
beta_H[9,2] 3.441 1.101 1.297 3.411 5.708
beta_H[10,2] 8.172 0.353 7.461 8.184 8.818
beta_H[11,2] 9.698 0.607 8.819 9.575 11.133
beta_H[12,2] 3.933 0.369 3.252 3.920 4.696
beta_H[13,2] 9.112 0.264 8.655 9.099 9.632
beta_H[14,2] 4.007 0.352 3.311 4.008 4.709
beta_H[15,2] 11.344 0.713 9.894 11.377 12.682
beta_H[16,2] 4.634 0.794 3.119 4.657 6.128
beta_H[1,3] 8.504 0.246 8.060 8.486 9.025
beta_H[2,3] 10.079 0.116 9.846 10.081 10.311
beta_H[3,3] 9.615 0.166 9.297 9.613 9.936
beta_H[4,3] -2.385 0.888 -4.142 -2.381 -0.642
beta_H[5,3] 3.893 0.606 2.616 3.914 5.060
beta_H[6,3] 8.172 1.241 6.475 7.798 10.796
beta_H[7,3] -2.585 0.701 -3.971 -2.575 -1.229
beta_H[8,3] 5.314 0.709 4.673 5.199 7.134
beta_H[9,3] -2.723 0.715 -4.137 -2.733 -1.324
beta_H[10,3] 8.741 0.278 8.216 8.732 9.304
beta_H[11,3] 8.559 0.271 7.974 8.578 9.038
beta_H[12,3] 5.251 0.321 4.460 5.290 5.777
beta_H[13,3] 8.814 0.184 8.439 8.823 9.158
beta_H[14,3] 5.677 0.275 5.081 5.693 6.159
beta_H[15,3] 10.361 0.327 9.719 10.356 11.016
beta_H[16,3] 6.468 0.618 5.100 6.540 7.460
beta_H[1,4] 8.284 0.175 7.905 8.297 8.593
beta_H[2,4] 10.135 0.120 9.874 10.141 10.358
beta_H[3,4] 10.116 0.165 9.751 10.128 10.407
beta_H[4,4] 11.761 0.441 10.892 11.769 12.623
beta_H[5,4] 5.574 0.795 4.321 5.477 7.382
beta_H[6,4] 7.113 0.915 5.075 7.371 8.391
beta_H[7,4] 8.223 0.346 7.551 8.230 8.885
beta_H[8,4] 6.667 0.323 5.870 6.696 7.120
beta_H[9,4] 7.203 0.467 6.266 7.210 8.092
beta_H[10,4] 7.754 0.238 7.315 7.745 8.259
beta_H[11,4] 9.291 0.203 8.900 9.290 9.703
beta_H[12,4] 7.135 0.211 6.727 7.130 7.574
beta_H[13,4] 9.006 0.146 8.711 9.009 9.280
beta_H[14,4] 7.655 0.219 7.224 7.662 8.081
beta_H[15,4] 9.445 0.238 8.969 9.447 9.895
beta_H[16,4] 9.199 0.222 8.819 9.182 9.675
beta_H[1,5] 8.980 0.142 8.686 8.983 9.245
beta_H[2,5] 10.780 0.094 10.607 10.776 10.977
beta_H[3,5] 10.924 0.178 10.603 10.918 11.294
beta_H[4,5] 8.402 0.467 7.520 8.389 9.353
beta_H[5,5] 5.377 0.615 3.927 5.428 6.433
beta_H[6,5] 8.773 0.623 7.896 8.636 10.276
beta_H[7,5] 6.787 0.328 6.144 6.783 7.461
beta_H[8,5] 8.224 0.259 7.852 8.195 8.800
beta_H[9,5] 8.217 0.471 7.277 8.212 9.172
beta_H[10,5] 10.080 0.229 9.606 10.083 10.515
beta_H[11,5] 11.545 0.231 11.094 11.542 11.993
beta_H[12,5] 8.478 0.194 8.094 8.483 8.866
beta_H[13,5] 10.013 0.131 9.751 10.014 10.261
beta_H[14,5] 9.183 0.241 8.742 9.172 9.687
beta_H[15,5] 11.179 0.249 10.694 11.178 11.664
beta_H[16,5] 9.944 0.164 9.615 9.946 10.258
beta_H[1,6] 10.184 0.192 9.834 10.170 10.602
beta_H[2,6] 11.513 0.106 11.298 11.515 11.718
beta_H[3,6] 10.804 0.162 10.444 10.812 11.092
beta_H[4,6] 12.861 0.832 11.190 12.877 14.500
beta_H[5,6] 5.925 0.628 4.774 5.904 7.219
beta_H[6,6] 8.771 0.657 7.140 8.874 9.765
beta_H[7,6] 9.827 0.554 8.753 9.817 10.936
beta_H[8,6] 9.496 0.355 8.736 9.530 9.971
beta_H[9,6] 8.459 0.787 6.900 8.454 10.027
beta_H[10,6] 9.513 0.309 8.832 9.537 10.055
beta_H[11,6] 10.804 0.355 10.039 10.828 11.432
beta_H[12,6] 9.377 0.255 8.880 9.366 9.922
beta_H[13,6] 11.066 0.161 10.771 11.060 11.400
beta_H[14,6] 9.860 0.291 9.277 9.866 10.409
beta_H[15,6] 10.853 0.432 10.014 10.855 11.702
beta_H[16,6] 10.553 0.222 10.053 10.565 10.951
beta_H[1,7] 10.853 0.887 8.692 10.971 12.260
beta_H[2,7] 12.205 0.430 11.321 12.207 13.045
beta_H[3,7] 10.532 0.674 9.065 10.585 11.705
beta_H[4,7] 2.546 4.225 -5.857 2.469 10.999
beta_H[5,7] 6.545 2.001 2.878 6.450 11.059
beta_H[6,7] 9.467 2.565 4.268 9.427 15.760
beta_H[7,7] 10.671 2.764 4.984 10.741 15.964
beta_H[8,7] 11.085 1.346 9.391 10.942 14.014
beta_H[9,7] 4.512 4.003 -3.533 4.575 12.084
beta_H[10,7] 9.833 1.418 7.270 9.753 12.920
beta_H[11,7] 10.969 1.736 7.825 10.835 14.916
beta_H[12,7] 9.995 0.920 7.837 10.063 11.601
beta_H[13,7] 11.676 0.761 9.925 11.760 12.892
beta_H[14,7] 10.489 0.955 8.391 10.552 12.253
beta_H[15,7] 12.189 2.244 7.778 12.175 16.615
beta_H[16,7] 12.073 1.173 10.185 11.880 14.854
beta0_H[1] 8.613 13.160 -18.119 8.673 35.704
beta0_H[2] 10.608 6.431 -2.240 10.657 22.455
beta0_H[3] 9.947 10.088 -9.923 10.090 30.889
beta0_H[4] 2.370 180.845 -348.881 0.894 364.155
beta0_H[5] 4.029 26.482 -51.177 4.505 53.793
beta0_H[6] 5.162 53.913 -109.445 7.336 108.908
beta0_H[7] 4.372 134.144 -266.155 4.296 278.757
beta0_H[8] 7.830 55.859 -19.169 6.743 40.795
beta0_H[9] 7.530 119.371 -231.706 7.299 259.066
beta0_H[10] 8.662 32.639 -59.021 9.658 75.591
beta0_H[11] 9.845 51.894 -92.914 9.323 115.161
beta0_H[12] 7.064 11.158 -14.401 6.741 31.354
beta0_H[13] 10.006 12.596 -10.810 9.923 32.905
beta0_H[14] 7.180 11.102 -16.166 7.162 30.613
beta0_H[15] 7.585 108.926 -222.976 7.030 219.246
beta0_H[16] 7.769 20.598 -36.097 7.957 50.831